Method and apparatus for measuring a three-dimensional curved surface shape

ABSTRACT

A method and apparatus for measuring a three-dimensional curved surface shape based on a new measuring principle that a surface of an object to be measured is coded with information relating to a slit light which is used as a medium and moved or rotated at a constant speed. The manner in which a linear reflected pattern of the slit light is moved over the surface of the object to be measured is picked up by a television camera to form a composite image in which a value of each of picture elements in the image is represented by information relating to the slit light, e.g., a position, time or projection angle of the slit light at an instant that the slit light passes through one of positions on the object surface corresponding to that picture element. Then, a difference in value between each corresponding picture elements of the composite image and another composite image formed similarly with respect to a reference plane is determined to measure a three-dimensional curve surface shape of the object to be measured.

This application is a continuation of application Ser. No. 259,037,filed Oct. 17, 1988 now abandoned.

BACKGROUND OF THE DISCLOSURE

The present invention relates to a method and apparatus for measuring athree-dimensional curved surface shape in a non-contact manner.

The measurement of three-dimensional curved surface shapes isconceivable for practical use in a wide range of applications such as athree-dimensional CAD input, robot vision, body contour measurement formedical and dressmaking purposes and various techniques have beenproposed in the past.

Particularly, one such technique well known as a light-section method oroptical cutting method is described for example on pages 398 and 399 of"Handbook for Image Processing" (Shokodo Co., Ltd.). As shown in FIG. 1of the accompanying drawings, this method notes a phenomemnon that whena slit Light 53 is projected from a slit light source 52 onto an object51 to be measured, a light beam pattern formed on the surface of theobject corresponds to the cross-sectional shape of the object 51 at theslit light projection position when the light beam pattern is observedfrom a direction different from the projecting direction and the methodhas been used widely by virtue of its simplicity, non-contactness andquantitative property.

When measuring the shape of a three-dimensional curved surface by thisoptical cutting method, while moving the slit light 53 in the directionsof an arrow 54, the resulting light beam patterns are observed by atelevision camera (55) and the thus generated video signal is processedfrom moment to moment, thereby extracting (56) the beam cutting lines(the shapes of the light beam patterns) within the image andreconstructing (57) the cutting lines to construct the curved surfaceshape.

While a method is known in which the construction of an optical systemincludes a light spot scanner as a light source in place of the slitlight source 52 and a high-speed light spot position detecting deviceknown as a PSD (position sensitive detector) sensor, for example, isused in place of the television camera 55, the basic principle is thesame as the one shown in FIG. 1.

While the above-mentional optical cutting method is one having variousadvantages, in order to detect and specify the respective points on anobject to be measured, the process of extracting the beam cutting lineswithin each image is essential and this causes the following problemsfrom the standpoint of measuring accuracy or reliability.

(1) Deterioration of the Measuring Accuracy and Spatial ResolutionDependent on the Shape of an Object to be Measured

With the optical cutting method, as shown in FIG. 2(a), if the surfaceof the object 51 to be measured in an inclined surface of an angle closeto a right angle with respect to the optical axis of the slit light 53,the width w of a light beam pattern at the object surface is narrow andit is possible to make a highly accurate measurement. However, if thesurface of an object to be measured is an inclined surface of an angleapproximately parallel to the optical axis of the slit light 53 as shownin FIG. 2(b), the width w of a light beam pattern at the object surfaceis increased so that not only is the uncertainty of the position duringthe beam cutting line increased with resulting deteriorated accuracy,but also the amount of movement of the light beam pattern on the objectsurface due to the movement of the slit light source 53 is increased,thereby simultaneouly deteriorating the spatial measuring resolution.

(2) Deterioration of the Measuring Reliability Due to the SurfaceReflectance of an Object to be Measured

With the optical cutting method, it is presupposed that during theprocess of extracting the beam cutting lines in a picture, the lightbeam pattern is sufficiently bright as compared with the ambientbrightness so that if, for example, there is a considerablenonuniformity in the reflectance of the object surface or alternativelythe angle of the inclined surface of the object surface is close to theoptical axis of the slit light, thus decreasing it reflected lightintensity, there are frequent cases where during the extraction of thebeam cutting lines the occurrence of discrete points is frequentlycaused or entirely wrong points are detected by mistaking them for thebeam cutting lines. Such a phenomenon is caused in cases where thereexists any background light other than the slit light during themeasurement, and each of such phenomena causes deterioration of themeasuring reliability or restricts the measuring environments of objectsto be measured.

As a result, due to some measuring problems arising from the beamcutting line extraction process, the optical cutting method has manyrestrictions from the application standpoint e.g., the shapes, thesurface contours and the environments of objects to be measured and itapplications are limited for its advantages including the simplicity,non-contactness, quantitativeness, etc. Thus, this method has not goneso far as to be assembled as a general-purpose three-dimensional curvedsurface shape measuring apparatus and put widely into practical use.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a three-dimensionalcurved surface shape measuring method and apparatus based on a newmeasuring principle which, while employing an optical system similar tothat used in the optical cutting method, introduces a new system ofusing a slit light moving or rotating at a constant speed as a medium tocode the surface of an object to be measured with information relatingto the slit light, thereby completely eliminating the need for the beamcutting line extracting process.

In accordance with the invention, a television camera picks up themanner in which the linear reflected pattern of a slit light is movedover the surface of an object to be measured so that each time the slitlight passes through the position on the surface of the objectcorresponding to each of the picture elements within the image, theinformation relating to the slit light, e.g., the position, time orlight projecting angle or the corresponding value is used as the valueof the picture element, thereby forming a composite image. Then, forexample, this composite image is compared with another composite imageproduced in a similar manner with respect to the reference planeexcluding the object to be measured to determine the difference in valuebetween each pair of corresponding picture elements of the two compositepictures and thereby to measure the three-dimensional curved surfaceshape of the object.

Thus, in accordance with the invention, while using the same opticalsystem of the optical system as the optical cutting method, even in thecase of an object to be measured having for example an inclined surfaceshape of an angle close to the projection angle of a slit light, thecomposite image of the object to be measured is compared with thecomposite image of the reference plane to determine the difference invalue between each pair of corresponding picture elements of the imagesand thereby to measure the three-dimensional shape therefore themeasurement of an such inclined surface can be effected with about thesame measuring accuracy and spatial resolution as the beam width or thesampling pitch of the slit light, thereby making it possible to measurethe shape of any object to be measured irrespective of its shape.

Further, in accordance with the invention, while the manner in which thelinear reflected pattern of the slit light is moved over the surface ofthe object to be measured is picked up by the television camera toperform an image composing processing in such a manner that the value ofeach of the picture elements within the image represents, for example,the position of the slit light at the instant that the slit light passesthrough the position on the object surface corresponding to that pictureelement, the only requisite condition for the establishment of the imagecomposing processing and the accurate determination of the shapeinformation is that each of the positions on the object to be measuredcorresponding to one of the picture elements has a brightness whichbecomes maximum at the instant that the slit light passes through thatposition.

As a result, not only variations in the surface reflectance of an objectto be measured have no effect on the measurement, but also thebrightness at each of the positions on the object surface becomesmaximum at the instant that the slit light passes through that positioneven if there exists background light so far as its light quantity isconstant in time and the brightness is such that the signal from thetelevision camera is not saturated, thereby ensuring the measurement isnot subject to the effects of the surface reflectance of the object tobe measured and the background light. Also, where the time is written asthe value of each picture element, no position detector is required andthe synchronizing signals of the television camera can be used as therequired timing signals.

Still further, in accordance with the invention, in addition to thecomposite image of the surface of the object to be measured and thecomposite image of the reference plane, a composite image of a secondreference plane is formed and the three-dimensional curved surface shapeof the object is measured on the basis of these composite images. Inthis way, by making the measurement through the provision of the tworeference planes, it is possible to make the measurement independentlyof the projection angle and scanning speed of the slit light, therebyenhancing the measuring accuracy.

Still further, in accordance with the invention, the composite images ofthe first and second reference planes are not formed at the time of eachmeasurement but they are preliminarily measured or obtained bycalculation and stored so that they are fetched and used when making themeasurement. When producing such composite images, by preliminarilyobtaining them by calculation, the operations during the measurement aresimplified.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram showing a conventional Light-sectionmethod or optical cutting method.

FIGS. 2(a) and (b) are diagrams showing the manners in which themeasuring accuracy of the conventional optical cutting method varies independence with the inclined surface angles.

FIGS. 3A and 3B are diagrams for explaining the measuring principles offirst and second embodiments of the invention.

FIGS. 4A and 4C are diagrams showing the construction of the opticalsystem according to the invention.

FIG. 5 is a block diagram showing the construction of thethree-dimensional shape measuring apparatus according to the firstembodiment of the invention.

FIG. 6 is an example of the measurement of an inclined surface shape.

FIG. 7 is a block diagram showing in detail the image processing circuitof FIG. 5.

FIG. 8 is a block diagram showing another example of the shapeprocessing circuit.

FIG. 9 is a block diagram showing the construction of thethree-dimensional shape measuring apparatus according to the secondembodiment of the invention.

FIG. 10 is a block diagram showing another example of the shapeprocessing circuit.

FIG. 11 is a digram showing the measuring principle of a thirdembodiment of the invention.

FIG. 12 is a schematic block diagram showing the construction of athree-dimensional shape measuring apparatus according to the thirdembodiment.

FIG. 13 shows an example of the measurement of an inclined surfaceshape.

FIG. 14 is a block diagram showing another example of the shapeprocessing circuit.

FIGS. 15A and 15B depiction of the relationship between these scanningdirections of the split light beams and the raster direction of thetelevision system.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Prior to describing first embodiment of the invention, its principlewill be first described conceptually with reference to FIGS. 3A and FIG.3B.

As shown in FIG. 3A, a slit light 3a spreading vertically to the paperplane is projected obliquely from above onto the surface of an object 2to be measured which is placed on a reference plane 1, and then theobject 2 is picked up by a television camera 8 from for example justabove the object 2 while moving the slit light 3a transverse to thepaper plane. At this time, the manner in which the linear reflectedpattern of the slit light 3a at the object surface is moved transverseto the image plane is observed on a television 8a monitor connected tothe television camera 8.

As mentioned previously, the linear shape of the reflected pattern ofthe slit light 3a reflects the irregularity information of the objectsurface and the conventional optical cutting method is designed so thatthe linear shape of the reflected pattern is sampled from moment tomoment and reconstructed, thereby measuring the three-dimensional shapeof the object to be measured.

In accordance with the invention, from the video signal generated by thetelevision camera 8 picking up the manner in which the linear reflectedpattern of the slit light 3a is moved over the surface of the object 2,a composite image is formed in which each of the picture elements withinthe image has a value representing the position of the slit light sourceat the instant that the slit light 3a passes through the position on theobject surface corresponding to that picture element or at the instantthat the brightness of that object surface position becomes maximum.

With the thus produced composite image, the values of its respectivepicture elements represent a height profile of the object surface basedon a plane A (hereinafter referred to as a virtual reference plane)shown by the dot-and-dash line in FIG. 3A. In this way, the heightprofile based on the virtual reference plane A of the object surface ismeasured.

However, generally the three-dimensional shape measurement of an objectmust measure the profile based on the positions on the plane on whichthe object 2 to be measured is placed (the reference plane of FIG. 3Awhich is hereinafter referred to as a reference plane) and not theprofile with respect to the virtual reference plane A in FIG. 3A.

To satisfy this requirement, it is necessary that after theabove-mentioned measurement with respect to the object surface has beenmade, thus measuring its height profile based on the virtual referenceplane A and then the object has been removed, the same measurement ismade with respect to the reference plane 1, thus measuring a heightprofile based on the virtual reference plane A and then, as shown inFIG. 3B, the difference in value between each pair of correspondingpicture elements of the two height profile images, i.e., the objectsurface composite image and the reference plane composite image, iscomputed. As the result of this processing, a height profile image onthe basis of the reference plane 1 is produced and the value of each ofthe picture elements of this height profile image is proportional to theheight of the corresponding position on the surface of the object to bemeasured which is based on the reference plane 1.

FIGS. 4A to 4C show the optical system of this invention and the object2 to be measured with an object plane. z=ƒ(x,y) is mounted on an x-yplane or the reference plane 1. With a z-axis as the optical axis, thetelevision camera 8 observes the object plane at a given angle, e.g.,from directly above. The slit light 3a spreading in the direction of ay-axis is projected at an angle θ with respect to an x-axis from theslit light source 3 and it is scanned in the x-axis direction. At thistime, the position of the slit light sources 3 is defined as a positionx=x_(o) at which the slit light 3a strikes against the reference plane 1(the following discussion also holds even if the position of the slitlight source 3 is defined on any plane provided that it is a planeparallel to the x-y plane. Here, the position of the slit light sourceis defined on the x-y plane for purposes of simplicity.) and thereforethe object surface and the plane of the slit light beam are respectivelydefined by the following expressions:

    Object surface: z=ƒ(x,y)                          (1)

    Plane of light beam: z={x-x.sub.o }·tan θ   (2)

Since the expressions (1) and (2) hold simultaneously on the line onwhich the light beam impinges on the object surface, the relation of thefollowing expression holds: ##EQU1##

The value u(x, y) of the composite image corresponding to thecoordinates (x, y) is given by the then current position x_(o) of theprojection of the light beam onto the reference plane 1, so that if u(x,y) is set equal to x_(o), the following expression holds: ##EQU2##

On the other hand, if u_(o) (x, y) represents the composite image of thereference plane (x-y plane) from which the object 2 to be measured hasbeen removed, the following expression holds by setting as setting ƒ(x,y)=0 in to equation (4):

    u.sub.o (x,y)=x                                            (5)

Therefore, the object profile ƒ(x, y) can be obtained in the form of thefollowing expression from equations (4) and (5):

    ƒ(x, y)={u.sub.o (x,y)-u(x,y)}·tan θ(6)

It is to be noted that the following methods may be easily conceived asexamples of the application of the present measuring principle. To beginwith, the first exemplary application is a method which establishes tworeference planes. More specifically, in addition to the previouslymentioned reference plane, there is provided a second reference planewhich is parallel to and separated by a distance d (the side close toand the other side away from the television camera are respectivelydesignated as + and -) from the former and a composite image issimilarly computed with respect to this reference plane. If thecomposite image with respect to the second reference plane isrepresented as u₁ (x, y), setting ƒ(x, y)=d in the expression (4), weobtain ##EQU3## Therefore, the object surface ƒ(x, y) can be obtainedfrom the expressions (4), (5) and (7) as follows: ##EQU4##

Also, as the second exemplary application, a method is conceivable whichis so designed that instead of providing a reference plane physically, acomposite image u_(o) (x, y) with respect to a virtual reference planeis obtained by computation from the expression (5) and then it issubstituted in the expression (6), thereby determining an object surfaceƒ(x, y). However, if, in this case, the horizontal axis (the rasterdirection) of the television camera picture forms an angle Φ with thescan direction of the slit light source, it is necessary to rotate theimage given by equation 5 by the angle Φ with reference to FIGS. 15A and15B depiction of the relationship between these scanning directions ofthe split light beams and the raster direction of the television systemand then use the resulting image given by the following equation:

    u.sub.o (x,y)=x cos Φ+y sin Φ                      (9)

Next, the first embodiment of the invention will be described withreference to FIGS. 5 to 7.

FIG. 5 shows the construction of a three-dimensional shape measuringapparatus according to the first embodiment. An object 2 to be measuredis mounted on a reference plane 1 serving as a basis of measurement. Aslit light source 3 is mounted on a linear stage 4 to project a slitlight 3a at an angle of projection θ onto the reference plane 1 and theobject 2 to be measured. With the slit light source 3 mounted on it, thelinear stage 4 is driven by a motor 6 controlled by a motor controller 5and thus the slit light source 3 is moved at a constant speed in adirection parallel to the reference plane 1.

At this time, the position of the slit light source 3 is measured by aposition sensor 7 incorporated in the linear stage 4, thereby enablingthe position control by the motor 5.

The reference plane 1 and the object 2 to be measured are picked up by atelevision camera 8 arranged in a manner that its optical axis crossesthe reference plane 1 at right angles and the resulting video signal isapplied to a shape measuring apparatus 9.

The shape measuring apparatus 9 mainly includes a shape processingcircuit 10 serving as image processing means for performing a shapeprocessing by image composing, and a sequence controller 11 for applyinga command to the motor controller 5 and performing a processing timingcontrol for the shape processing circuit 10.

During the shape measurement, the shape measuring apparatus 9 drives thelinear stage 4 through the sequence controller 11 responsive to anexternally applied start signal and the slit light source 3 is set inits initial position. Thereafter, the scanning of the slit light source3 is started.

The shape processing circuit 10 includes in its input section an imagecomposing circuit 12 which will be described later so that at the sametime that the scanning by the slit light source 3 is started, the videosignal applied from the television camera 8 is processed from moment tomoment and an image composing processing is performed such that thevalue of each of the picture elements within the image is represented bya stage position signal generated at the instant that the image of theslit light passes through that picture element. Then, upon thecompletion of one scanning of the slit light source 3, its result u(x,y) is transferred to an object surface composite image memory 13.

Then, after the object 2 has been removed from the reference plane 1,the sequence controller 11 returns the slit light source 3 to theinitial position and the scanning by the slit light source 3 is againstarted. The image composing circuit 12 performs the same imagecomposing processing as performed with respect to the object 2 for thereference plane 1 so that upon the completion of the scanning by theslit light source, its result u_(o) (x, y) is transferred to a referenceplane composite image memory 14.

After these image composing processings have been completed, in responseto the commands from the sequence controller 11 the shape processingcircuit 10 computes through a difference image processing circuit 15 animage representing the difference in value between every pair ofcorresponding picture elements of the images respectively stored in theobject surface composite image memory 13 and the reference planecomposite image memory 14 in the form of

    {u.sub.o (x,y)-u(x,y)}

which in turn is calibrated or corrected in height profile through theuse of a height correcting circuit 16 and the thus obtained resultantheight profile data

    {u.sub.o (x,y)-u(x,y)}·tan θ

is stored in a three-dimensional shape memory 17. In response to acommand from a higher-rank computer or a CAD system, the height profiledata stored in the three-dimensional shape memory 17 is suitablytransferred to the computer or the CAD system.

With the present embodiment, if, for example, the object 2 having theinclined surface of an angle close to the projection angle of the slitlight is measured as shown in FIG. 6, due to the slope of the inclinedsurface being so close to the projection angle of the slit light, whenthe slit light reaches the position designated at "1" in FIG. 6, thewhole inclined surface is brightened uniformly and the stored contentsof the object surface composite image memory 13 become as shown byreference numeral 13a. The stored contents of the reference planecomposite image memory 14 become as shown by reference numeral 14a.Therefore, these image data are processed by the difference imageprocessing circuit 15 and the height correcting circuit 16 so that theresulting data stored in the three-dimensional shape memory 17 becomesas shown by reference numeral 17a. It will thus be seen that asatisfactorily high resolution is ensured even in the case of such shapehaving a surface close to the angle of the slit light.

It has been difficult in the past to extract the beam cutting lines fromthe image 13a and the application of the optical cutting method to suchinclined surface cannot provide the required measuring accuracy andspatial resolution. In accordance with the present embodiment, even inthe case of such an inclined surface the measurement can be effectedwith a measuring accuracy and spatial resolution of the order of thebeam width or the sampling pitch of the slit light and generally thedesired shape measurement can be realized irrespective of the shape ofan object to be measured.

FIG. 7 is a block diagram showing an example of the image processingcircuit 12 forming a constituent element of the shape measuringapparatus 9.

The image composing circuit 12 includes a maximum brightness imageprocessing unit 18 for processing the video signal applied from thetelevision camera 8 to compute the brightness of each of the pictureelements at the instant that it attains the maximum brightness, and acomposite image processing unit 19 for performing an image composingprocessing such that the value of each picture element represents thetime instant that the brightness of each picture element becomesmaximum, as well as a synchronizing circuit 20, a memory addressgenerating circuit 21 and an output control circuit 22 for the purposeof controlling the former.

The maximum brightness image processing unit 18 includes mainly amaximum brightness image memory 23 composed of a buffer memory formaximum brightness image processing purposes as well as an A/D convertercircuit 24 responsive to the timing signal generated from thesynchronizing circuit 20 to digitize the video signal by A/D conversion,a maximum brightness image memory 25 for controlling the reading andwriting of data into the maximum brightness memory addresses designatedby the memory address generating circuit 21, a comparator circuit 26 forcomparing the values of each pair of corresponding picture elements ofthe image inputted from the television camera and the image in themaximum brightness image memory to select and output the greater of thetwo values, and a switch circuit 27.

On the other hand, the composite image processing unit 19 includesmainly a composite image memory 28 for storing the result of compositeimage processing as well as a composite image memory control circuit 29having a function of responding to the output signal from the comparatorcircuit 26 of the maximum brightness image processing unit 18 so thatwhen the input signal level from the television camera is greater thanthe value of the picture element at the corresponding address of themaximum brightness image memory 23, the stage position signal is writteninto the composite image memory 28.

This circuit functions so that starting at the timing of beginning ofthe processing with the maximum brightness image memory 23 and thecomposite image memory 28 being cleared to zero, while digitizing theinput video signal from the television camera by using the A/D convertercircuit 24, the value of each of the picture elements of the videosignal is compared with the value of that picture element in the maximumbrightness image memory 23 which corresponds to the position of theformer picture element so that only when the value of the video signalis greater, is the value of the picture element in the maximumbrightness image memory 13 updated by the value of the video signal andsimultaneously the stage position signal is written into thecorresponding picture element of the composite image.

In this way, during the time that is commanded by the externally appliedprocessing control signal, the above-mentioned processing is performedso that the previously mentioned desired image is formed in thecomposite image memory 28 upon the completion of the processing. Thethus processed composite image is transferred to the followingprocessing circuit through the output control circuit 22.

While, in the above-described embodiment, the composite image of thereference plane 1 is formed during the measurement, it is necessary toform the composite image of the reference plane 1 only once andtherefore the initially formed composite image of the reference plane 1can be used as such during the second and subsequent measurements. Inaddition, the composite image of the reference plane 1 is so simple inconstruction that the shape processing circuit 10 may be provided withan additional processing function such that a virtual reference plane isobtained by calculation from equation (5) to produce and store itscomposite image in the reference plane composite image memory 14.

Further, whereas in the above-described embodiment a single referenceplane is provided, a second reference plane may be provided in additionto the reference plane 1. The second reference plane (not shown) ispositioned between the reference plane 1 and the slit light source 3 andat a distance d from the reference plane 1.

In this case, as shown in FIG. 8, a composite image u₁ (x, y) accordingto the second reference plane is formed in the same way as mentionedpreviously by the image composing circuit 12 and a composite imagememory 14A for storing this composite image is provided in addition tothe object surface composite image memory 13 and the reference compositeimage memory 14. Also, the difference image processing circuit 15 andthe height correcting circuit 16 are replaced with a processing circuit30 for performing the calculation of the previously mentioned equation(8).

A second embodiment of the invention will now be described. Whereas inthe first embodiment the position of the slit light source 3 at theinstant that the slit light passes through each picture element is codedas the value of that picture element, in accordance with the secondembodiment the time at that instant is coded and its measuring principleis basically the same as the first embodiment. In FIGS. 4A to 4C, theslit light source 3 projects at the angle θ the slit light 3a spreadingin the y-axis direction to scan at a constant speed v in thex-direction. As a result, those expressions corresponding to equations(2) to (7) and (9) in the first embodiment are also respectivelyobtained by the similar procedures in the second embodiment in the formof the following expressions (2a) to (7a) and (9a): ##EQU5## where t isthe amount of time elapsed after the slit light beam scanning begins andv is the scanning speed of the slit light beam.

It is to be noted that equations (1), (8) and (9) of the firstembodiment can also be used as such in the second embodiment.

FIG. 9 is a schematic block diagram of the three-dimensional shapemeasuring apparatus according to the second embodiment which is soconstructed that the timing signals for an image composing circuit 12are produced by separating the vertical synchronizing signals of thevideo signal applied from a television camera 8 by a sync separationcircuit 121 and counting the separated signals by a counter circuit 122starting at the same time that the scanning by a slit light source 3 isbegun.

A shape processing circuit 10 includes the image composing circuit 12 inthe input section whereby an image composing processing is performed sothat simultaneously with the beginning of the scanning of the slit lightsource 3, the video signal inputted from the television camera 8 isprocessed from moment to moment so as to represent the value of each ofthe picture elements in the image by the time instant at which the imageof the slit light passes through that picture element and upon thecompletion of each scanning of the slit light source 3 the processingresult u(x, y) is transferred to an object surface composite imagememory 13.

Then, after the object 2 to be measured has been removed from areference plane 1, a sequence controller 11 returns the slit lightsource 3 to the initial position and the scanning by the slit lightsource 3 is again started. The image composing circuit 12 performs onthe reference plane 1 the same image composing processing as performedon the object 2 so that upon completion of the scanning by the slitlight source 3 the processing result u_(o) (x, y) is transferred to areference plane composite image memory 14.

After the completion of these image composing processings, the shapeprocessing circuit 10 responds to the command from the sequencecontroller 11 to compute by a difference image processing circuit 15 animage

    {u.sub.o (x, y)-u(x, y)}

representing the difference in the values of the corresponding pictureelements of the image in the object surface composite image memory 13and the image in the reference plane composite image memory 14 and thenthe height profile is corrected by means of a height correcting circuit16, thereby storing the resulting height profile data

    {u.sub.o (x, y)-u(x, y)}·v·tan θ

in a three-dimensional shape memory 17.

In response to the command from a higher-rank computer or a CAD system,the height profile data stored in the three-dimensional shape memory 17is suitably transferred to the computer or the CAD system.

As in the case of the first embodiment shown in FIG. 6, also in thisembodiment second the stored contents of the object surface compositeimage memory 13 and the reference plane composite image memory 14 becomeas shown at numerals 13a and 14a, respectively. As a result, these imagedata are processed by the difference image processing circuit 15 and theheight correcting circuit 16 so that the height profile image shown atnumeral 17a is obtained and stored in the three-dimensional shape memory17.

Whereas in the embodiment of FIG. 9 a single reference plane isprovided, a second reference plane may be provided in addition to thereference plane 1 as in the embodiment of FIG. 8. The second referenceplane (not shown) is arranged between the reference plane 1 and the slitlight source 3 so as to be separated from the reference plane 1 by adistance d.

In this case, as shown in FIG. 10, the shape processing circuit 10 isdesigned so that a composite image u₁ (x, y) of the second referenceplane is formed by the image composing circuit 12 in a like manner asmentioned previously and a composite image memory 14a for storing it isprovided in addition to the object surface composite image memory 13 andthe reference plane composite image memory 14. Also, a processingcircuit 30 for performing the calculation of the previously mentionedequation (8) is provided in place of the difference image processingcircuit 15 and the height correcting circuit 16.

Next, a third embodiment of the invention will be described. Themeasuring principle of this embodiment will be described firstconceptually with reference to FIG. 11.

As shown in FIG. 11, a slit light 3a spreading in the vertical directionto the paper plane is projected obliquely from above onto the surface ofan object 2 to be measured which is placed on a reference plane 1 andthe object surface is picked up by a television camera 8 from forexample just above the object 2 to be measured while moving the slitlight 3a transversely to the paper plane by use for example of arotating mirror 4A. At this time, the manner in which the linearreflected pattern of the slit light on the object surface is movedtransversely in the image is observed on a television monitor 8aconnected to the television camera 8.

As mentioned previously, the linear shape of the reflected pattern ofthe slit light 3a reflects the irregularity information of the objectsurface and the conventional optical cutting method measures thethree-dimensional shape of the object to be measured by extracting thelinear shape of the reflected pattern from moment to moment andreconstructing the extracted linear shapes.

In accordance with the present invention, on the basis of the videosignal generated from the television camera 8 which picks up the mannerin which the linear reflected pattern of the slit light 3a is moved overthe object surface, a composite image is formed in which the value ofeach of the picture elements in the image represents the slit lightprojection angle at the instant that the slit light passes through theposition on the object surface corresponding to that picture element.

The resulting composite image is such that the value of each of thepicture elements corresponds to the angle of elevation obtained when thecenter of the slit light rotation of the rotating mirror 4A is looked upfrom the position on the object surface corresponding to the pictureelement. Thus, if the composite image is represented in terms of θ(x, y)by using the coordinate system (x, y) of the corresponding objectsurface, the profile ƒ(x, y) of the object surface can be obtained fromthe following equation by a simple geometrical calculation based on FIG.11:

    ƒ(x, y)=z.sub.o -(x.sub.0 -x)·tan θ(x, y)(10)

It is to be noted that the following measuring methods may be easilyconceived as examples of the application of the above-mentionedmeasuring principle. To begin with, the first exemplary application is amethod in which the above-mentioned measurement is made with respect tothe reference plane 1 and the resulting composite image is utilized toeliminate the the parameter x_(o) or z_(o). In other words, by settingƒ(x, y)=0 in equation (10), the composite image θ_(o) (x, y) of thereference plane 1 becomes as follows: ##EQU6##

Therefore, by eliminating the parameter z_(o) or z_(o) from equation(10), the object surface profile ƒ(x, y) is determined by the relationsof the following equations: ##EQU7##

On the other hand, the second exemplary application is a method in whichthe above-mentioned measurement is made with respect to two referenceplanes ƒ(x, y)=0 and ƒ(x, y)=d and the resulting composite images areutilized to eliminate both of the parameters x_(o) and z_(o). In otherwords, as regards the composite image θ₁ (x, y) of the second referenceplane, the following equation is obtained by setting ƒ(x, y)=d inequation (10): ##EQU8##

Therefore, by substituting the relations of equations (11) and (14) inequation (10) to eliminate the parameters x_(o) and z_(o), ƒ(x, y) isdetermined in the form of the following equation: ##EQU9##

It is to be noted that while, in accordance with the invention, thesurface of an object to be measured is coded in terms of slit lightprojection angles, as the means for this purpose, the slit lightprojection angles need not always be measured directly and it ispossible to temporarily code the surface of the object to be measured bythe equivalent values such as the rotation angles of the rotating mirroror the times after the start of the scanning of the rotating mirror onthe condition that the rotation speed of the rotating mirror is contantand then convert them to slit light projection angles by processing.

Further, as will be seen from equations (10) to (15), the compositeimage θ(x, y) coded in terms of the slit light projection angles isgenerally used in the form of its tangent tan θ(x, y) in all thesubsequent shape processing operations and therefore during the initialimage composing period coding may be effected directly in terms of thetangents of slit light projection angles in place of the slit lightprojection angles.

The third embodiment of the invention will now be described withreference to FIGS. 12 and 13.

FIG. 12 shows the construction of a three-dimensional shape measuringapparatus according to the third embodiment. An object 2 to be measuredis placed on a reference plane 1 used as a reference for measurements.The slit light emitted from a slit light source 3 is reflected by arotating mirror 4A and projected onto the object 2 obliquely from above.The rotating mirror 4A is driven by a motor 6 controlled by a motorcontroller 5 in such a manner that the slit light 3a scans all over thesurface of the object 2 on the reference plane 1.

At this time, it is assumed that the position (x_(o), z_(o)) of thecentral axis of rotation of the rotating mirror 4A relative to thereference plane 1 is measured accurately. Also, the angle formed by therotating mirror 4A with the reference plane 1 is detected by a rotationangle sensor 7 operatively mounted on the shaft of the motor 6 andapplied to a shape measuring apparatus 9 through the motor controller 5,thereby computing the slit light projection angle θ varying from momentto moment with respect to the object 2 to be measured.

On the other hand, the surface of the object 2 is picked up by atelevision camera 8 arranged so that its optical axis crosses thereference plane 1 at right angles and the resulting video signal isapplied to the shape measuring apparatus 9.

The shape measuring apparatus 9 mainly includes a shape processingcircuit 10 serving as image processing means for performing a shapeprocessing by image combining, a beam projection angle computing circuit33 for computing a slit light beam projection angle θ from the output ofthe rotation angle sensor 7 and applying it to the shape processingcircuit 10, and a sequence controller 11 for applying commands to themotor controller 5 and controlling the timing of processing of the shapeprocessing circuit 10.

When making the shape measurement, the shape processing apparatus 9drives the motor 6 through the sequence controller 11 in accordance withthe externally applied start signal and the rotating mirror 4A is set inthe initial position. Thereafter, the rotation of the rotating mirror 4Ais started and the scanning by the slit light source 3a is started.

The shape processing circuit 10 includes an image composing circuit 12in the input section whereby during each scanning period of the slitlight source 3a, an image composing processing is performed so that uponthe starting of the scanning by the slit light source 3a, the videosignal applied from the television camera 8 is processed from moment tomoment and the beam projection angle at the instant that the slit lightpasses through each of the picture elements in the image is read by thebeam projection angle computing circuit 41 to represent the value ofeach picture element.

After the processing of the composite image θ(x, y) has been completed,in accordance with the command from the sequence controller 11 the shapeprocessing circuit 10 computes a height profile ƒ(x, y) by means of aheight processing circuit 40 in accordance with equation (10) and theresulting data is stored in a three-dimensional shape memory 17.

In accordance with the command from a higher-rank computer or a CADsystem, the height profile data stored in the three-dimensional shapememory 17 is suitably transferred to the computer or the CAD system.

In accordance with this embodiment third, if, for example, themeasurement is made on the object 2 to be measured which has an inclinedsurface of an angle close to the beam projection angle of the slit lightas shown in FIG. 13, the slope of the inclined surface is very close tothe projection angle of the slit light so that when the slit lightarrives at the position designated as "1" in FIG. 13, the whole inclinedsurface is brightened uniformly. However, if the resulting angle codedcomposite image is processed in accordance with equation (10), suchmeasured results as shown in FIG. 13, are obtained. From this it will beseen that a satisfactorily high resolution can be ensured even in thecase of a shape having a surface close to the angle of a slit light.

While in the past it has been difficult to extract the beam cuttinglines from such image as explained previously and it has been impossibleto expect the desired measuring accuracy and spatial resolution by theapplication of the optical cutting method to the measurement of suchinclined surface, in accordance with this embodiment a measuringaccuracy and a spatial resolution of about the same degree as the beamwidth or sampling pitch of a slit light are possible and generally thedesired shape measurements can be effected irrespective of the shapes ofobjects to be measured.

Whereas in the above-described embodiment, the height processing circuit34 performs the calculation of equation (10), the parameter z_(o) orx_(o) in equation (10) may be eliminated so as to enhance the measuringaccuracy.

In this case, a composite image is also determined with respect to thereference plane 1 in a similar manner as the object to be measured andit is represented as θ(x, y). Then, as shown in FIG. 14, the compositeimage θ_(o) (x, y) of the object to be measured and the composite imageθ_(o) (x, y) of the reference plane are temporarily stored in the objectsurface composite image memory 13 and the reference plane compositeimage 14, respectively, and then the calculation of equation (12) or(13) is performed by the height processing circuit 34, therebydetermining the three-dimensional shape.

Also, both of the parameters z_(o) and x_(o) in equation (10) may beeliminated. In this case a second reference plane (which is parallel toand separated by a distance d from the reference plane 1) is provided inaddition to the reference plane 1 so that a composite image θ_(o) of theobject 2 to be measured, a composite image θ_(o) (x, y) of the referenceplane 1 and a composite image θ₁ (x, y) of the second reference planeare all produced in a similar manner and are temporarily stored in theobject surface composite image memory 13, the reference plane compositeimage memory 14 and a second reference plane composite image memory 14A.Then, the calculation of equation (15) is performed by the heightprocessing circuit 34 to determine a three-dimensional shape.

It is to be noted that the composite images of the reference plane 1 andthe second reference plane need not be produced again and therefore theinitially produced composite images can be used as such during thesecond and subsequent measurements. Also, in view of the fact that thecomposite images of the reference plane 1 and the second reference planeare both simple in construction, the shape processing circuit 10 may beprovided with processing functions such that virtual reference planesare obtained by calculation in accordance with equations (11) and (14)to produce their respective composite images and store them in thememories 14 and 14A, respectively.

What is claimed is:
 1. A method of measuring a three-dimensional curvedsurface shape, comprising the steps of:causing a linear slit light toscan a surface of an object to be measured on a reference plane;producing video signals by picking up the surface of said object using atelevision camera; inputting said video signals corresponding to aplurality of picture elements into a memory means; forming a compositeimage of the surface of said object by composing an image in whichsuccessive video signals of the same picture element are compared inmagnitude to renew the same picture element in said memory means usingas a value thereof information relating to scanning of said slit lightat a time of application of the larger of said compared video signalsand to thereby represent a value of each picture element in said memorymeans by information relating to scanning of said slit light at a timewhen said slit light passes respectively through a measuring pointcorresponding to each of said picture elements; and measuring athree-dimensional curved surface shape of said object in accordance withsaid composite image.
 2. A measuring method according to claim 1,wherein said television camera is aimed in a direction perpendicular tosaid reference plane.
 3. A measuring method according to claim 2,wherein the step of measuring a three-dimensional curved surface shapeof said object comprises measuring said three-dimensional curved surfacein accordance with the difference between the values of the pictureelements for said composite image of said object and the values of thecorresponding picture elements for a preliminarily determined compositeimage of said reference plane.
 4. A measuring method according to claim3, wherein the step of causing a linear slit light to scan the surfaceof said object comprises causing said linear slit light to scan linearlythe surface of said object, said linear slit light being projected froma direction which forms an angle θ with said reference plane, wherein θis not equal to 90°.
 5. A measuring method according to claim 2, whereinthe step of causing a linear light to scan the surface of said objectcomprises the steps of causing said linear slit light to scan thesurface of said object by reflection from a rotatable mirrorandmeasuring angles of projection of said slit light, wherebyinformation relating to scanning of said slit light is represented by aslit light projection angle at an instant when said slit light passesthrough a measuring point corresponding to one of said picture elementof by a value equivalent thereto.
 6. An apparatus for measuring athree-dimensional curved surface shape comprising:slit light projectingmeans for projecting a linear slit light onto a surface of an object tobe measured on a first reference plane from a direction forming an angleθ with said first reference plane which is not equal to 90°; slit lightscanning means for causing said linear slit light to scan the surface ofsaid object on said first reference plane; a television camera forpicking up the surface of said object from a direction different fromthe direction of projection of said slit light projecting means; imagecomposing means for composing a composite image of the surface of saidobject by composing an image in which successive video signals of thesame picture element are applied from said television camera andcompared in magnitude to renew said same picture element in a memorymeans by using as a value thereof information relating to scanning ofsaid slit light at a time of application of the larger of said comparedvideo signals, whereby a value of each of said picture elements in saidmemory means is represented by said respective information relating toscanning of said slit light at an instant when said slit light passesthrough a measuring point corresponding to said respective pictureelement; and image processing means for measuring a three-dimensionalcurved surface shape in accordance with said composite image of saidobject.
 7. A measuring apparatus according to claim 6, wherein saidimage composing means comprises:maximum brightness memory means forstoring a maximum level of said video signal for each of said pictureelements during a predetermined period of time; maximum brightness imageprocssing means for comparing said video signal and the signals storedin said maximum brightness memory means for each picture element thereofand writing a value of the greater one thereof in said maximumbrightness memory means; composite image memory means for storing avalue of a synchronizing signal or external input signal at an instantwhen the magnitude said video signal is greatest for each of saidpicture elements during a predetermined time period; and composite imageprocessing means for storing in said composite image memory means aninstantaneous synchronizing signal count value or external signal valuefor each picture signal count value or external signal value for eachpicture element for which said maximum brightness memory meansdetermines that said video signal is greater than said signal stored insaid maximum brightness memory means.
 8. A measuring apparatus accordingto claim 6, wherein said slit light scanning means linearly scans saidslit light all over the surface of said object and wherein said imageprocessing means measures a three-dimensional curved surface shape ofsaid object in accordance with the difference between the values of thepicture elements of said composite image of said object and the valuesof the picture elements of a preliminarily determined composite image ofsaid first reference plane.
 9. A measuring apparatus according to claim8, wherein said television camera is aimed in a direction perpendicularto said first reference plane.
 10. A measuring apparatus according toclaim 8, wherein said image processing means determines athree-dimensional shape f(x, y) of said object on the basis of acomposite image u(x, y) of said object, a composite image u_(o) (x, y)of said first reference plane and a composite image u₁ (x, y) withrespect to a second reference plane which is parallel to and separatedby a distance d from said first reference plane in accordance with theequation. ##EQU10## where x and y are the positional coordinates of thepicture elements.
 11. A measuring apparatus according to claim 8,wherein said image processing means determines a three-dimensional shapef(x, y) of said object on the basis of a composite image u(x, y) of saidobject, a composite image u_(o) (x, y) of said first reference plane, aslit light projection angle θ with respect to said first reference planeand a slit light scanning speed v in accordance with the equation:

    f(x, y)={u.sub.o (x, y)-u(x, y)}v tan θ,

where x and y are the positional coordinates of the picture elements.12. A measuring apparatus according to claim 8, further comprising slitlight angle measuring means for measuring a projection angle of saidslit light, wherein said slit light scanning means rotates said slitlight projecting means within a plane of said slit light beam about anaxis of rotation consisting of a straight line parallel to said firstreference plane to scan said slit light all over the surface of saidobject, andsaid formation relating to scanning of said slit light is aslit light projection angle or a value equivalent thereto.
 13. Ameasuring apparatus according to claim 12, wherein said image processingmeans determines a three-dimensional shape f(x, y) of said objectaccording to two-dimensional coordinates x and y on the basis of acomposite image θ(x, y) of said object and a horizontal displacementx_(o) and vertical displacement z_(o) of said axis of rotation of saidslit light relative to an origin of said first reference plane inaccordance with the equation:

    f(x, y)=z.sub.o -(x-x.sub.o) tan θ(x, y)


14. A measuring apparatus according to claim 12, wherein said imageprocessing means determines a three-dimensional shape f(x, y) of saidobject according to two-dimensional coordinates x and y at least on thebasis of a composite image u(x, y) of said object surfaces and apreliminarily determined composite image θ_(o) (x, y) of said firstreference plane.
 15. A measuring apparatus according to claim 12,wherein said large processing means determines a three-dimensional shapef(x, y) of said object according to two-dimensional coordinates x and yon the basis of a composite image θ(x, y) of said object, a compositeimage θ_(o) (x, y) of said first reference plane and a horizontaldisplacement x_(o) of said axis of rotation of said slit light relativeto an orgin of said reference plane in accordance with the equation:

    f(x, y)={tan θ.sub.o (x, y)-tan θ(x, y)}(x.sub.o -x)


16. A measuring apparatus according to claim 12, wherein said imageprocessing means determines a three-dimensional shape f(x, y) of saidobject according to two-dimensional coordinates x and y on the basis ofa composite image θ(x, y) of said object, a composite image θ_(o) (x, y)of said first reference plane and a vertical displacement z_(o) of saidaxis of rotation of said slit light relative to an origin of saidreference plane in accordance with the equation: ##EQU11##
 17. Ameasuring apparatus according to claim 12, wherein said image processingmeans determines a three-dimensional shape f(x, y) of said objectaccording to two-dimensional coordinates x and y a composite image θ₀(x, y) of said first reference plane and a composite image θ₁ (x, y) ofa second reference plane which is parallel to and separated by a distaned from said first reference plane in accordance with the equation:##EQU12##
 18. An apparatus for measuring a three-dimensional curvedsurface shape comprising:slit light projecting means for projecting alinear slit light onto a surface of an object to be measured on a firstreference plane from a direction forming and angle θ with said firstreference plane which is not equal to 90°; slit light scanning means forcausing said linear slit light to scan the surface of said object onsaid first reference plane; a television camera for picking up thesurface of said object from a direction different from the direction ofprojection of said slit light projecting means; image composing meansfor composing a composite image of the surface of said object bycomposing an image in which video signals of the same picture elementare successively applied from said television camera and successivelycompared in magnitude so as to renew said same picture element in amemory means by using a value thereof information relating to scanningof said slit light at a time of application of the greater one of saidcompared video signals, whereby a value of each of said picture elementsin said memory means is represented by said respective informationrelating to scanning of said slit light at an instant when said slitlight passes through a measuring point corresponding to said respectivepicture element; image processing means for measuring athree-dimensional curved surface shape in accordance with said compositeimage of said object; said slit light scanning means linearly scanningsaid slit light all over the surface of said object and said imageprocessing means measures a three-dimensional curved surface shape ofsaid object in accordance with the difference between the values of thepicture elements of said composite image of said object and the valuesof the picture elements of a preliminarily determined composite image ofsaid first reference plane; and said image processing means determines athree-dimensional shape f(x, y) of said object on the basis of acomposite image u(x, y) of said object, a composite image u_(o) (x, y)of said first reference plane and said slit light projection angle θwith respect to said first reference plane in accordance with theequation:

    f(x, y)=(u.sub.o (x, y)-u(x,y)) tan θ

where x and y are the positional coordinates of the picture elements.